2x^2+24x-1178=0

Solution for 2x^2+24x-1178=0 equation:

Simplifying
2x2 + 24x + -1178 = 0

Reorder the terms:
-1178 + 24x + 2x2 = 0

Solving
-1178 + 24x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-589 + 12x + x2) = 0

Factor a trinomial.
2((-31 + -1x)(19 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-31 + -1x)' equal to zero and attempt to solve:

Simplifying
-31 + -1x = 0

Solving
-31 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '31' to each side of the equation.
-31 + 31 + -1x = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -1x = 0 + 31
-1x = 0 + 31

Combine like terms: 0 + 31 = 31
-1x = 31

Divide each side by '-1'.
x = -31

Simplifying
x = -31
Subproblem 2
Set the factor '(19 + -1x)' equal to zero and attempt to solve:

Simplifying
19 + -1x = 0

Solving
19 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-19' to each side of the equation.
19 + -19 + -1x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1x = 0 + -19
-1x = 0 + -19

Combine like terms: 0 + -19 = -19
-1x = -19

Divide each side by '-1'.
x = 19

Simplifying
x = 19
Solution
x = {-31, 19}